Question

Prove for an isothermal isobaric system, the particles can only move from the region of higher Gibbs free energy to the region of lower Gibss free energy,

Answer 1

First let´s recall the definition of Gibss free energy:

G = H - TS

For a process ocurring we can exprees it like this:

from the second law of thermodynamics we know that the universe entropy is always raising up meaning =

also

since we have isothermal process, entalphy is zero, then we have

so

This means that Energy of gibbs for spontaneus process will allways be negative meaning that energy is going from higher to lower, particles in the system can only move from higher gibbs free energy to lower gibss free energy.